So why is everyone giving these guys so much clout at the expense of the majority of the population?

The GOP and its RW media branch manufactured a narrative of an independent, nonpartisan, grassroots social movement when what the "Tea Party" really was was just a top-down mirage driven by the pro-corporate establishment hard right of the previously discredited GOP that needed to be rebranded.  The GOP was able to pull this off because they have strong institutional capacity built up over decades and are often able to drive the narrative most of the rest of the media gloms onto. The MSM largely went along with this narrative.  The opposition has, with the exception of a few weeks in the spring relating to the events in Madison, been unable to generate a counter-narrative of any strength.

Then the President super-empowered the GOP's hard right ("Tea Party") by legitimizing their terrorist tactics and negotiating with them while retreating, instead of standing up to them or maneuvering them into destroying themselves, as Clinton did with the Gingrich Congress on his budget fights.  It may well be the case that he has no possibility of being able to do this at this point, having shown himself to be a pushover and, increasingly, a non-leader in the eyes of much of the public.   

And, of course, a public that is too economically illiterate, too passive, too unorganized, and too easily fooled is the essential precondition for all of this.

Thus, the train wreck.

Understanding what has happened may be a necessary first step towards turning things around. 

It might be that one useful thing that could be done would be for commentators and bloggers to stop using the term "Tea Party", as though it is something different from the Republican radical right wing. 

Instead of using the phrase "Tea Party", which connotes something distinct and independent from the unpopular Republican party, why not use a phrase like the "radical Republican right-wing" or "far right Republicans" or "the Republican far-right"?  Name, accurately, the folks who are pushing us off the cliff.  In other words, don't play along with their efforts to rebrand their trash, but counter it instead.  Make it clear to the public who is pushing this destructive agenda.